Closest pair for any of a huge number of points

Question

We are given a huge set of points in 2D plane. We need to find, for each point the closest point within the set. For instance suppose the initial set is as follows:

Answer 1

The traditional approach is to preprocess the data and put it in a data structure, often a K-d tree, for which the "nearest point" query is very fast.

There is an implementation in the nnclust package.

library(nnclust)
foo <- cbind(x=c(1,2,4,4,10),y=c(1,2,4,4,10))
i <- nnfind(foo)$neighbour
plot(foo)
arrows( foo[,1], foo[,2], foo[i,1], foo[i,2] )